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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 26 Dec 2010 11:18:28 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/26/t1293362200bvejmyw8dowh584.htm/, Retrieved Mon, 06 May 2024 20:37:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115522, Retrieved Mon, 06 May 2024 20:37:01 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Autocorrelatie functie

Estimated Impact

154

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Variance Reduction Matrix] [Unemployment] [2010-11-29 09:29:57] [b98453cac15ba1066b407e146608df68]
- RMPD  [(Partial) Autocorrelation Function] [Workshop 9 (ACF p=0)] [2010-12-15 13:59:06] [845827b7f02503df17c96f445745fee7]
-         [(Partial) Autocorrelation Function] [] [2010-12-16 16:02:02] [24bb5b06bd1854f48aebec8f44957ed0]
-    D        [(Partial) Autocorrelation Function] [Paper] [2010-12-26 11:18:28] [e247a0a17f1c9a5b89239760575ef468] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115522&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115522&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115522&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.851873	6.6533	0
2	0.631712	4.9338	3e-06
3	0.498858	3.8962	0.000123
4	0.462024	3.6085	0.000311
5	0.487997	3.8114	0.000162
6	0.483454	3.7759	0.000182
7	0.399486	3.1201	0.00138
8	0.278093	2.172	0.016877
9	0.171724	1.3412	0.092412
10	0.144404	1.1278	0.131903
11	0.202386	1.5807	0.059561
12	0.218955	1.7101	0.046166
13	0.0548	0.428	0.335079
14	-0.139961	-1.0931	0.139317
15	-0.255812	-1.998	0.025093
16	-0.295174	-2.3054	0.012281
17	-0.279659	-2.1842	0.016401

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.851873 & 6.6533 & 0 \tabularnewline
2 & 0.631712 & 4.9338 & 3e-06 \tabularnewline
3 & 0.498858 & 3.8962 & 0.000123 \tabularnewline
4 & 0.462024 & 3.6085 & 0.000311 \tabularnewline
5 & 0.487997 & 3.8114 & 0.000162 \tabularnewline
6 & 0.483454 & 3.7759 & 0.000182 \tabularnewline
7 & 0.399486 & 3.1201 & 0.00138 \tabularnewline
8 & 0.278093 & 2.172 & 0.016877 \tabularnewline
9 & 0.171724 & 1.3412 & 0.092412 \tabularnewline
10 & 0.144404 & 1.1278 & 0.131903 \tabularnewline
11 & 0.202386 & 1.5807 & 0.059561 \tabularnewline
12 & 0.218955 & 1.7101 & 0.046166 \tabularnewline
13 & 0.0548 & 0.428 & 0.335079 \tabularnewline
14 & -0.139961 & -1.0931 & 0.139317 \tabularnewline
15 & -0.255812 & -1.998 & 0.025093 \tabularnewline
16 & -0.295174 & -2.3054 & 0.012281 \tabularnewline
17 & -0.279659 & -2.1842 & 0.016401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115522&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.851873[/C][C]6.6533[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.631712[/C][C]4.9338[/C][C]3e-06[/C][/ROW]
[ROW][C]3[/C][C]0.498858[/C][C]3.8962[/C][C]0.000123[/C][/ROW]
[ROW][C]4[/C][C]0.462024[/C][C]3.6085[/C][C]0.000311[/C][/ROW]
[ROW][C]5[/C][C]0.487997[/C][C]3.8114[/C][C]0.000162[/C][/ROW]
[ROW][C]6[/C][C]0.483454[/C][C]3.7759[/C][C]0.000182[/C][/ROW]
[ROW][C]7[/C][C]0.399486[/C][C]3.1201[/C][C]0.00138[/C][/ROW]
[ROW][C]8[/C][C]0.278093[/C][C]2.172[/C][C]0.016877[/C][/ROW]
[ROW][C]9[/C][C]0.171724[/C][C]1.3412[/C][C]0.092412[/C][/ROW]
[ROW][C]10[/C][C]0.144404[/C][C]1.1278[/C][C]0.131903[/C][/ROW]
[ROW][C]11[/C][C]0.202386[/C][C]1.5807[/C][C]0.059561[/C][/ROW]
[ROW][C]12[/C][C]0.218955[/C][C]1.7101[/C][C]0.046166[/C][/ROW]
[ROW][C]13[/C][C]0.0548[/C][C]0.428[/C][C]0.335079[/C][/ROW]
[ROW][C]14[/C][C]-0.139961[/C][C]-1.0931[/C][C]0.139317[/C][/ROW]
[ROW][C]15[/C][C]-0.255812[/C][C]-1.998[/C][C]0.025093[/C][/ROW]
[ROW][C]16[/C][C]-0.295174[/C][C]-2.3054[/C][C]0.012281[/C][/ROW]
[ROW][C]17[/C][C]-0.279659[/C][C]-2.1842[/C][C]0.016401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115522&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115522&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.851873	6.6533	0
2	0.631712	4.9338	3e-06
3	0.498858	3.8962	0.000123
4	0.462024	3.6085	0.000311
5	0.487997	3.8114	0.000162
6	0.483454	3.7759	0.000182
7	0.399486	3.1201	0.00138
8	0.278093	2.172	0.016877
9	0.171724	1.3412	0.092412
10	0.144404	1.1278	0.131903
11	0.202386	1.5807	0.059561
12	0.218955	1.7101	0.046166
13	0.0548	0.428	0.335079
14	-0.139961	-1.0931	0.139317
15	-0.255812	-1.998	0.025093
16	-0.295174	-2.3054	0.012281
17	-0.279659	-2.1842	0.016401

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.851873	6.6533	0
2	-0.342587	-2.6757	0.004781
3	0.281684	2.2	0.015802
4	0.104558	0.8166	0.208661
5	0.183441	1.4327	0.078521
6	-0.105369	-0.823	0.206868
7	-0.110327	-0.8617	0.196119
8	-0.069015	-0.539	0.295916
9	-0.073003	-0.5702	0.285328
10	0.129358	1.0103	0.158166
11	0.13958	1.0902	0.139966
12	-0.190305	-1.4863	0.071171
13	-0.54826	-4.2821	3.3e-05
14	0.184358	1.4399	0.077507
15	-0.08753	-0.6836	0.248398
16	-0.133697	-1.0442	0.150255
17	-0.087721	-0.6851	0.247932

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.851873 & 6.6533 & 0 \tabularnewline
2 & -0.342587 & -2.6757 & 0.004781 \tabularnewline
3 & 0.281684 & 2.2 & 0.015802 \tabularnewline
4 & 0.104558 & 0.8166 & 0.208661 \tabularnewline
5 & 0.183441 & 1.4327 & 0.078521 \tabularnewline
6 & -0.105369 & -0.823 & 0.206868 \tabularnewline
7 & -0.110327 & -0.8617 & 0.196119 \tabularnewline
8 & -0.069015 & -0.539 & 0.295916 \tabularnewline
9 & -0.073003 & -0.5702 & 0.285328 \tabularnewline
10 & 0.129358 & 1.0103 & 0.158166 \tabularnewline
11 & 0.13958 & 1.0902 & 0.139966 \tabularnewline
12 & -0.190305 & -1.4863 & 0.071171 \tabularnewline
13 & -0.54826 & -4.2821 & 3.3e-05 \tabularnewline
14 & 0.184358 & 1.4399 & 0.077507 \tabularnewline
15 & -0.08753 & -0.6836 & 0.248398 \tabularnewline
16 & -0.133697 & -1.0442 & 0.150255 \tabularnewline
17 & -0.087721 & -0.6851 & 0.247932 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115522&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.851873[/C][C]6.6533[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.342587[/C][C]-2.6757[/C][C]0.004781[/C][/ROW]
[ROW][C]3[/C][C]0.281684[/C][C]2.2[/C][C]0.015802[/C][/ROW]
[ROW][C]4[/C][C]0.104558[/C][C]0.8166[/C][C]0.208661[/C][/ROW]
[ROW][C]5[/C][C]0.183441[/C][C]1.4327[/C][C]0.078521[/C][/ROW]
[ROW][C]6[/C][C]-0.105369[/C][C]-0.823[/C][C]0.206868[/C][/ROW]
[ROW][C]7[/C][C]-0.110327[/C][C]-0.8617[/C][C]0.196119[/C][/ROW]
[ROW][C]8[/C][C]-0.069015[/C][C]-0.539[/C][C]0.295916[/C][/ROW]
[ROW][C]9[/C][C]-0.073003[/C][C]-0.5702[/C][C]0.285328[/C][/ROW]
[ROW][C]10[/C][C]0.129358[/C][C]1.0103[/C][C]0.158166[/C][/ROW]
[ROW][C]11[/C][C]0.13958[/C][C]1.0902[/C][C]0.139966[/C][/ROW]
[ROW][C]12[/C][C]-0.190305[/C][C]-1.4863[/C][C]0.071171[/C][/ROW]
[ROW][C]13[/C][C]-0.54826[/C][C]-4.2821[/C][C]3.3e-05[/C][/ROW]
[ROW][C]14[/C][C]0.184358[/C][C]1.4399[/C][C]0.077507[/C][/ROW]
[ROW][C]15[/C][C]-0.08753[/C][C]-0.6836[/C][C]0.248398[/C][/ROW]
[ROW][C]16[/C][C]-0.133697[/C][C]-1.0442[/C][C]0.150255[/C][/ROW]
[ROW][C]17[/C][C]-0.087721[/C][C]-0.6851[/C][C]0.247932[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115522&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115522&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.851873	6.6533	0
2	-0.342587	-2.6757	0.004781
3	0.281684	2.2	0.015802
4	0.104558	0.8166	0.208661
5	0.183441	1.4327	0.078521
6	-0.105369	-0.823	0.206868
7	-0.110327	-0.8617	0.196119
8	-0.069015	-0.539	0.295916
9	-0.073003	-0.5702	0.285328
10	0.129358	1.0103	0.158166
11	0.13958	1.0902	0.139966
12	-0.190305	-1.4863	0.071171
13	-0.54826	-4.2821	3.3e-05
14	0.184358	1.4399	0.077507
15	-0.08753	-0.6836	0.248398
16	-0.133697	-1.0442	0.150255
17	-0.087721	-0.6851	0.247932

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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